This invention relates to a grid producing apparatus for producing grid points for use in discreting a space on numerically solving a partial differential equation.
On numerically solving a partial differential equation, discreted grid is produced which is for use in dividing an analytic region into a plurality of micro-regions in order to obtain simultaneous equations approximating to the partial differential equation. On obtaining the simultaneous equations, use may be made of a finite element method or a finite difference method. On calculating an electric characteristic of a semiconductor device, the finite element method is used in which micro-regions are defined which are charged by the discreted grid points, respectively. In the finite element method, a test function may be used which has "1" in each of the micro-regions and "0" in other regions. Such a finite element method may be called a control volume method. Each of the micro-regions may be called a control volume (CV) region in the control volume method.
On stably solving the partial differential equation, it is necessary to prevent the CV regions from overlap. Furthermore, it is necessary to prevent each of the CV regions from passing a boundary between one analytic region and another analytic region.
On producing the discreted grid, a grid producing method is disclosed as a first conventional method in Japanese Patent Publication Tokkai Syo 64-86078 (86078/1989). Furthermore, another grid producing method is disclosed as a second conventional method in IEEE Trans. Computer-Aided-Design, Vol. 8, No. 5, 1989.
However, it is difficult to obtain the discreted grid for use in stable numerical analysis in each of the first and the second conventional methods as will be described later.